[1] Likewise in other lexica. The headword is present participle of περίειμι (from εἰμί "I am"), neuter nominative/accusative singular. It must be quoted from somewhere; there are numerous possibilities. (The genitive occurs in the quotation which follows.)
[2] At pi 2979, where this quotation is repeated in part, the participle is in the neuter plural (πεπορισμένα ) instead of the feminine accusative plural seen here. Gaisford deleted the second προῖκα in this entry.
[3] Quotation (transmitted, in Adler's view, via the Excerpta Constantini Porphyrogeniti) unidentifiable. Jonathan Toup (1713-1785) attributed it to Cassius Dio and claimed a connection with chi 501, but see the note there.